A Mathematical Model of Aluminum Depth Filtration with Ceramic Foam Filters: Part II. Application to Long-Term Filtration

The mathematical model to compute the efficiency of depth filtration of molten aluminum, previously presented in Part I, was further developed and applied to study long-term filtration. In this case, the incoming suspension entering the unit cell was not assumed homogeneous, and the times and positions of particle at the inlet were obtained stochastically from a random number generator. The particles that were transported by the fluid flow to the wall and collided against this surface remained attached to the wall and accumulated within the domain. The accumulation of particles decreased the effective area for fluid to flow through the pore, causing distortion of the overall velocity field in the domain. The flow field was obtained from the numerical solution of the continuity and Navier-Stokes equations for transient flow, the particle trajectories were calculated using the Langrangian motion equation including the buoyancy, and the viscous drag force corrected for the wall effect. The model predicted a preferred particle accumulation around the windows to form a cake of particles and the effect that inclusion accumulation has on the flow field, pressure drop, and filtration coefficient. This work studied the influence of particle concentration and fluid velocity on the evolution of the filtration coefficient and pressure drop. It was found that these quantities were practically constant for TiB2 particles suspended in aluminum at a concentration of 1 ppm and filtered during 60 minutes through the unit cell of a 30 ppi foam filter. However, at a particle concentration of 10 ppm, the model predicted that the filtration coefficient and pressure drop changed appreciably for the same period of filtration. The results, obtained from first principles, provide a rationale to explain fluctuations of the filtration coefficient and pressure drop, reported in the literature, without introducing any empirical or probability factor in the respective equations.